Without green card or AP they will not be admitted back to the US.
Might try to contact local US embassy. But I highly doubt they will do anything within 4 days so be prepared to reschedule that flight.

As far as I know expedite for AOS doesn't exist. Pretty much - you're in the US already, so you don't have to worry about expediting your way there.
Also without actual orders on papers, there won't grand any kind of expedites.
I assume you mean your foreign spouse not yourself - as a "military personnel" you don't do AOS yourself. 😛 And your foreign spouse is not a military personnel.

Too late.
You need to apply for spouse visa now. ETA 12 - 14 months.
She doesn't have tourist visa anymore. That was canceled when she filled for AOS.
There is nothing you can do now. AOS - abandoned and canceled. She will NOT be allowed back in the US without a proper spouse visa.
Shame. She screwed up this situation pretty badly.

Yeah this is what I thought. So the only route you can do is:
- Apply for spouse visa. ETA 12 - 14 months.
- Arrive in the US to activate the visa and receive a green card (you need copy of green card for naturalization)
- File for naturalization
- Apply for expedite of naturalization.

Wait... what?
I believe this is NOT how this all work.
You cannot.. file for immigrant visa and citizenship at the same time.
@geowrian @missileman This is not a possible scenario at all, right?
Question 1.
She has to enter the US, pay the green card fee, wait for green card to arrive.
Question 2.
No... it's not.
You cannot naturalize from... tourist visa.